Warm Up A 2009 study investigated whether people can tell the difference between pate, processed meats and gourmet dog food. Researchers used a food processor to make similar spreads of all the foods. 50 participants tasted all 5 foods and guessed which they thought was dog food. The data is below. Duck Pate Spam Dog Food Pork Pate Liverwurst 3 11 8 6 22 If the participants guessed randomly the proportion choosing each meat should be 0.20. Test the hypothesis that significantly more people chose liverwurst than would have through random guessing.

Warm Up Revisited A 2009 study investigated whether people can tell the difference between pate, processed meats and gourmet dog food. Researchers used a food processor to make similar spreads of all the foods. 50 participants tasted all 5 foods and guessed which they thought was dog food. The data is below. Duck Pate Spam Dog Food Pork Pate Liverwurst 3 11 8 6 22 Are these results inconsistent with the hypothesis that people were simply guessing which one was the dog food?

Practice A cell phone company sells protective cases in seven different colors. The company wonders if the same number of cases of each color are sold. They took a random sample of 200 sales over the past month and recorded the color of each case. The data is below. Is this data convincing evidence that the proportion of sales for at least one color is not the same? Blue Red Green Yellow Purple White Black 32 26 20 18 27 36 41 1) State appropriate hypotheses. 2) Create a table of observed and expected counts. 3) Calculate c2, df, and the p-value and make a conclusion.

Activity – Are the Proportions of Colors of M&Ms the Same as Advertised? According to the Mars candy company M&M milk chocolate candies are produced in the following proportions of colors (for candies produced at the Cleveland plant). Red Orange Yellow Green Blue Brown .131 .205 .135 .198 .207 .124 We will run a Chi Square Goodness of Fit test to see if our bag of M&M’s follows these proportions. Reference: SAS blog - The distribution of colors for plain M&M candies.

Activity – Are the Proportions of Colors of M&Ms the Same as Advertised? Each table group will be given a sample of M&M candies. Count the number of candies of each color and put this value on the board. Also write the total number of candies you have. Treat the data with respect – DON’T EAT IT YET!!

Activity – Are the Proportions of Colors of M&Ms the Same as Advertised? Use the combined data from the class to determine if this is convincing evidence that the proportion of at least one color of M&Ms is not the same as advertised. 1) State appropriate hypotheses. 2) Create a table of observed and expected counts. 3) Calculate c2, df, and the p-value and make an appropriate conclusion. After your analysis is complete, please dispose of your data in an appropriate manner.